Not in any practical way, no. A flash drive requires flash memory. The BIOS memory on your PC motherboard might be adaptable... but even if you can get those chips free you'd need to throw enough other circuitry around them to interface them that it'd be a hassle, and the result would be tiny compared to off-the-shelf thumb drives.

Given that a 4gig thumb drive is available for $15 -- less, if you get a no-name -- building your own really isn't worth the effort. The cost of parts, and the value of your time, would be higher than that.